Calabi-Yau algebras are very important in mathematics: as well as turning up naturally in representation theory and topology, they are noncommutative examples of Calabi-Yau varieties which play a central role in string theory. Lately, fractional Calabi-Yau algebras have risen in prominence. These are a more restrictive class of algebras which have very good homolgical properties. They connect abstract algebra, category theory, and noncommutative geometry. They can often be described using quivers (directed graphs) together with relations.
The aim of this project is to construct a variety of new examples of these algebras. Particular tools include the methods of higher homological algebra, as well as methods inspired by mathematical physics. This project would suit a student who likes abstract algebra, but is also interested in explicit computations. There are possibilities to use computer software in the research if that is of interest to the candidate.
It may be possible to undertake this PhD project on a part time basis but applicants should discuss with Dr Grant in the first instance
Applications are processed as soon as they are received and the project may be filled before the closing date, so early application is encouraged.